Covariant action for conformal higher spin gravity

Abstract

Conformal higher spin (HS) gravity is a HS extension of Weyl gravity and is a family of local HS theories, which was put forward by Segal and Tseytlin. We propose a manifestly covariant and coordinate-independent action for these theories. The result is based on an interplay between HS symmetries and deformation quantization: a locally equivalent but manifestly background-independent reformulation, known as the parent system, of the off-shell multiplet of conformal HS fields (Fradkin–Tseytlin fields) can be interpreted in terms of Fedosov deformation quantization of the underlying cotangent bundle. This brings into the game the invariant quantum trace, induced by the Feigin–Felder–Shoikhet cocycle of Weyl algebra, which extends Segal’s action into a gauge invariant and globally well-defined action functional on the space of configurations of the parent system. The same action can be understood within the worldline approach as a correlation function in the topological quantum mechanics on the circle.